What is the derivative of left- x-1 right- x-2-10Derivative does not exist1

Question

What is the derivative of left- x-1 right-  x-2-10Derivative does not exist1

Toppr Admin · Accepted Answer

Given f-x-x-x2212-1-f-x-x-x2212-1- when x-x2212-1-gt-0 i-e- x-gt-1f-x-x2212-x-x2212-1-1-x2212-x when x-x2212-1-lt-0 i-e- x-lt-1So- at x-2-f-x-x-x2212-1dfdx-1Thus- derivative of f at x-2 is 1-

What is the derivative of $| x - 1 |$ at $x = 2$ ?
$- 1$
$0$
Derivative does not exist
$1$

given $f (x) = | x - 1 |$
$f (x) = (x - 1)$ when $x - 1 > 0$ i.e. $x > 1$
$f (x) = - (x - 1) = 1 - x$ when $x - 1 < 0$ i.e. $x < 1$
So, at $x = 2, f (x) = x - 1$
$\frac{d f}{d x} = 1$
Thus, derivative of $f$ at $x = 2$ is $1$ .

What is the derivative of |x−1| at x=2?−10Derivative does not exist1

given f(x)=|x−1|f(x)=(x−1) when x−1>0 i.e. x>1f(x)=−(x−1)=1−x when x−1<0 i.e. x<1So, at x=2,f(x)=x−1dfdx=1Thus, derivative of f at x=2 is 1.

What is the derivative of $| x - 1 |$ at $x = 2$ ?
$- 1$
$0$
Derivative does not exist
$1$

given $f (x) = | x - 1 |$
$f (x) = (x - 1)$ when $x - 1 > 0$ i.e. $x > 1$
$f (x) = - (x - 1) = 1 - x$ when $x - 1 < 0$ i.e. $x < 1$
So, at $x = 2, f (x) = x - 1$
$\frac{d f}{d x} = 1$
Thus, derivative of $f$ at $x = 2$ is $1$ .